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Operator norm
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, the operator norm measures the "size" of certain <a href="/facts/Linear_operator/Q1PBKNVV">linear operators</a> by assigning each a <a href="/facts/Real_number/R02gw5Pb">real number</a> called its operator norm. Formally, it is a <a href="/facts/Norm_(mathematics)/xIbR4uE1">norm</a> defined on the space of <a href="/facts/Bounded_linear_operator/LYmDTIqR">bounded linear operators</a> between two given <a href="/facts/Normed_vector_space/rmDljfyE">normed vector spaces</a>. Informally, the operator norm ‖ T ‖ {\displaystyle \|T\|} of a linear map T : X → Y {\displaystyle T:X\to Y} is the maximum factor by which it "lengthens" vectors. </p>